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The door code to gain access to a top-secret laboratory is 6 digits. The first 3 digits of the code are all odd, and the last 3 digits are all even. Digits can be used more than once. How many possible codes are there?

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apologiabiology
5 odd numbers and 5 even numbers
since they can be repeated
5*5*5=first 3 digits
5*5*5=last 3 digits
in all
5*5*5*5*5*5=15625 ways

Possible (Outcomes) number of codes are 15625.

What are possible outcomes?

"Possible Outcomes – a list of all the resulting possibilities from an event."

Let's work this out first looking at the first three digits of the code, which are all odd and can be used more than once.

First three digits

There are five odd numbers: 1, 3, 5, 7, 9.

Let's look at the first number in the code - it can be any one of five numbers, so we have 5 choices.

The next number in the code has the same number of choices, so we have 5 choices.

And the same goes for the last number, with 5 choices.

Put together, we have

Possible outcomes for first three digits

= 5 × 5 × 5

= 125

Last three digits

There are also five even numbers: 0, 2, 4, 6, 8

This means we'll also have 125 ways to arrange the even numbers.

Possible outcomes for last three digits

= 125

Putting it together

That's 125 ways in the first set of three and 125 in the second set of three, and so it's

∴ Possible(Outcomes) number of codes

= 125 × 125

= 15625

As an aside, we could have looked at each digit in the code, seen there were 5 choices for each digit, and so calculated

[tex]5^{6}[/tex] = 15625

Hence, possible(Outcomes) number of codes are 15625.

Learn more about possible (outcomes) here

https://brainly.com/question/19567251

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